cog

The root cog is unusual: it carries one prefix — Latin co- ('together, thoroughly') — into two different verbs of the mind, and from that single intensifier two whole families branch out.

The thinking branch — cōgitāre. Take co- ('thoroughly') and fuse it with agitāre ('to drive, stir, set in motion'). Latin cōgitāre literally meant 'to stir things thoroughly in the mind' — to turn an idea over and over, the way you'd agitate water. That image of mental churning gives us:

- cogitate — to think deeply, to ponder. The pure root verb: sitting and stirring your thoughts.
- ex- (out) + cogitate → excogitate — to think something out, to devise an answer by hard reflection. Where cogitate is open-ended pondering, excogitate aims at a result you finally produce.
- in- (not) + cogit + -ant → incogitant — not doing the stirring; thoughtless, inconsiderate.

Notice the family secret: agitate itself is a near cousin. When you cogitate, you are quietly 'agitating' ideas inside your head.

The knowing branch — cognōscere. Now take the same co- and attach it to gnōscere ('to know'). Cognōscere meant 'to know thoroughly, to get acquainted with.' English absorbed this as the cogn- words:

- re- (again) + cogn + -ition → recognition — to know again: you meet something a second time and your mind matches it to the first. From there it grew two everyday senses — recognizing a face (identification) and recognizing someone's achievement (acknowledgment).
- cognizance — the state of knowing, of being aware. 'To take cognizance of' something is formal English for 'to take notice of, to be aware of.'
- cognomen — co- + (g)nōmen ('name'): literally a name by which a person is known. In ancient Rome it was the third, family-branch name (the 'Cicero' in Marcus Tullius Cicero); today it loosely means a surname, epithet, or nickname.

The cogn- branch is huge beyond this batch: cognition and cognitive (the act and faculty of knowing), recognize, and incognito (in- 'not' + cognito — moving about un-known, with your identity hidden) all belong here.

The deeper link. gnōscere ('know') is the Latin cousin of Greek gignōskein, the source of gnost/gn- words like diagnosis ('knowing-through') and prognosis. So the cogn- branch is family with every gn- 'know' word in English. And because cōgitāre hides agitāre, the thinking branch is a distant relative of agitate.

The rule of the family: spot co- fused to a mind-verb. If the second part is about stirring/thinking (cogit), it's the pondering branch; if it's about knowing (cogn), it's the recognition branch. Either way, co- is telling you the mental work is being done thoroughly.